With the rapid increases in both scale and complexity of virtual environments, an efficient navigation capability becomes critical in virtual reality systems. This is particularly true in medical applications, which require navigation through complex structures such as the colon, aorta, lungs and the like. This implies the presence of efficient flight-path planning. Many known navigation techniques focus primarily on a planned navigation mode, where a movie is computed by automatically moving a virtual camera along a precomputed flight path from a start point of a virtual object to an end point of the object and generating a sequence of navigation frames. Centerline algorithms are often used as the flight path to give wide views at the object center. Such algorithms are useful when the virtual environment depicts a luminar structure, such as a colon or artery.
The following properties are considered desirable for a flight-path planning:                (1) To obtain a wide view of the virtual environment, the path should stay away from the surface.        (2) The path should be a one-voxel-wide simple path without any 2D manifolds or self-intersection.        (3) Any two adjacent voxels on the path should be directly connected, i.e., at most one, two, or three of their 3D coordinates differ by one, forming a 6-, 18-, or 26-connected path.        (4) The path planning procedure should be fast and automatic, which frees the user from having to engage in the data processing.        
There has been a great deal of research on flight-path planning techniques based on an object centerline or a set of connected centerlines, generally referred to as a skeleton. Most of the centerline extraction algorithms can be divided into three categories: manual extraction, distance mapping, and topological thinning.
Manual extraction, which requires the user to manually mark the center of each object region slice by slice, neither satisfies property 4 nor guarantees property 3. It may violate property 1, because a center point in a 2D slice may not lie along the medial axis in the 3D space.
Distance mapping often employed Dijkstra's shortest path algorithm to extract the centerline or flight path rapidly with full automation. This technique generally satisfies properties 2 through 4. Unfortunately, it does not satisfy property 1, because the shortest path tends to hug corners at high-curvature regions. Efforts have been made to push the shortest path towards the object center by post-remedy. However, such efforts have not completely solved the problem, or involve distance function adjustment based on other measurements, and are computationally complex and expensive.
Topological thinning generates center paths by peeling off a volumetric object layer by layer until there is only one central layer left. This technique satisfies properties 1 through 3 very well, but it does not satisfy property 4, due to the expensive processing iteration. Paik et al. have accelerated this technique by incorporating the above shortest path method in parallel with a thinning procedure. However, the manual detection of the tip for each branches in this technique needs to be improved. This is described Automatic Flight Planning for Virtual Endoscopy”, Medical Phys., 1998, 25(5), 629-637.